Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7?
A.100^15
B.200^15
C.100^56
D.10,000^15
The correct answer is A. 100^15.
The Product Rule of Exponents states that when multiplying two powers with the same base, you can add their exponents.
In this case, we have 100^8 multiplied by 100^7. Since both powers have the same base (100), we can add their exponents:
100^8 * 100^7 = 100^(8 + 7) = 100^15
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The correct answer is C. 100^56.
The Product Rule of Exponents states that when multiplying two powers with the same base, you can add their exponents.
In this case, we have 100^8 multiplied by 100^7. Since both powers have the same base (100), we can add their exponents:
100^8 * 100^7 = 100^(8 + 7) = 100^15
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To simplify the expression using the Product Rule of Exponents, we add the exponents together.
In this case, we have 100^8 ⋅ 100^7.
Using the Product Rule, we add the exponents 8 and 7:
100^8 ⋅ 100^7 = 100^(8+7).
The sum of the exponents is 15.
So, the correct simplification of the expression is 100^15.
Therefore, the correct answer is A. 100^15.
To simplify the expression 100^8⋅100^7 using the Product Rule of Exponents, we add the exponents when multiplying two numbers with the same base.
In this case, the base is 100, and the exponents are 8 and 7.
So, using the product rule, we add the exponents: 8 + 7 = 15.
Therefore, the simplified expression is 100^15.
The correct answer is A. 100^15.